摘 要
磁浮系統是一個高度非線性且開迴路不穩定的系統。本論文以直流電磁鐵式之磁浮系統為控制對象，並以定位控制為控制目的。
首先利用相位領先控制器作為系統的內迴路，藉以穩定系統；之後，再設計一模糊PID控制器作為系統的外迴路，以克服系統的非線性及改善系統的響應性能。
由於設定模糊PID控制器的參數是一件冗長的嘗試錯誤法，故本文採用非二進位改良型基因演算法來幫助我們設定及最佳化其參數。實驗結果顯示，經由改良型基因演算法所設計出的模糊PID控制器不僅增加了磁浮系統的操作範圍，且能迅速準確的定位，同時並具有抗外來干擾的能力。
此外，相較於其他的控制理論，本文所使用的控制方法也較容易設計及實施。

Abstract
Magnetic suspension systems are highly nonlinear and essentially unstable systems. In this thesis, we facilitate the position control problem for the DC electromagnetic suspension system.
We utilize a phase-lead controller operating in the inner loop to stabilize the system first, and try to design a PID fuzzy logic controller (PIDFLC) operating in the outer loop to overcome the nonlinearity of the system and to improve the system’s performance.
Since the work of setting fuzzy control parameters is a long-winded trial and error, we adopt non-binary modified GAs to help us setting and optimizing parameters. As experimental results show that the designed PIDFLC not only increases the system’s operating range, but also positions accurately and rapidly; meanwhile, it has the ability to eliminate extra disturbance.
In addition, comparing with other control theories, the control method which we utilize is easier to be implemented.

Contents I
List of Symbols IV
List of Figures VI
List of Tables VIII
Chinese Abstract IX
English Abstract X

Chapter 1. Introduction and Papers Review 1
1.1 Research Motivation and Goal 1
1.2 Papers Review 1
1.3 Genetic Algorithms and Fuzzy Logic Controller 2
1.4 Research Results and Contributions 3
1.5 Thesis Structure 4

Chapter 2. Concerning about Genetic Algorithms 5
2.1 Brief History of Genetic Algorithms 5
2.2 Foundations of Genetic Algorithms 6
2.3 Simple Genetic Algorithms (SGA) 8
2.4 Modifications to Simple Genetic Algorithms 11
2.4.1 Encoded and Decoded Processes 12
2.4.2 Fitness Function Definition 12
2.4.3 Fitness Scaling 13
2.4.4 Reproduction(Selection) Operator 15
2.4.5 Crossover Operator 16
2.4.6 Mutation Operator 17
2.4.7 Elitist Strategy 18
2.4.8 Extinction and Immigration Strategy 19
2.4.9 The Structure of Modified Genetic Algorithms 21

Chapter 3. Concerning about Fuzzy Systems and Control 23
3.1 Introduction of Fuzzy Systems and Control 23
3.2 Fuzzy Sets and Membership Function 26
3.3 Simplified Fuzzy Reasoning Method 28
3.4 Hybrid Reduced Rule Fuzzy PID Like Controller 31

Chapter 4. System Modeling and Hybrid Reduced Rule Fuzzy PID Controller Design 35
4.1 System Modeling and Linearization 35
4.2 Hybrid Reduced Rule Fuzzy PID Controller Design 41
4.2.1 The Phase Lead Compensator 41
4.2.2 Suggestions about Design of PIDFLC Using GAs 44
4.2.3 Design Steps and Simulation for PIDFLC by
Simultaneous Design of Membership Functions
and Rule Bases Using GAs 46

Chapter 5. Experiments and Results 51
5.1 Experimental Apparatus 51
5.2 Experimental Steps 56
5.3 Experimental Results 57

Chapter 6. Conclusions and Recommendations 64

References 66

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